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MATLAB: An Introduction with Applications

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

**Find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.**

**Two-tailed test, α = 0.05**

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The critical value(s) is/are z = [___]

*(Round to two decimal places as needed. Use a comma to separate answers as needed.)*

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**Explanation:**

For a two-tailed test with a significance level of α = 0.05, you will find the critical values by determining the z-scores that correspond to the upper and lower tails of the standard normal distribution that contain 2.5% of the data on each side (because 0.05 divided by two equals 0.025).

Typically, this results in critical z-scores of approximately ±1.96.

**Graph Explanation:**

The graph for this problem would depict a standard normal distribution curve (bell-shaped) where the rejection regions are shaded at both tails. Each rejection region would contain 2.5% of the data, and the area in the middle (non-rejected region) would contain 95% of the data under the curve. The critical values (z-scores) of approximately ±1.96 mark the boundaries between the rejection and non-rejection regions.

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